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Lesson 5, Topic 1
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# Meaning of Work, Energy and Power

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### Work:

Work can be defined as the product of force and distance through which an object moves in the direction of force applied.

Work (W) = Force (F) x distance (D)

= Newton x metre

= Joule (J)

1J = 1Nm

If the object doesn’t move, then no work is done.

Where Force is the product of mass and gravity or mass and acceleration (F = mg, or F = ma) (g = 10m/s2)

The unit of work is Joule named after the scientist, James Prescott Joule, who did a lot of experiments with energy.

In the illustration above, the work done is the product of the force (12N) used to push the box and the distance (5m).

= 12N x 5m = 60J

Joules Converter:

Larger units are KiloJoule (KJ) and MegaJoule (MJ)

1,000 Joules (J) = 1 KiloJoule (KJ)

1,000,000 Joules (J) = 1 MegaJoule (MJ)

1,000 KiloJoules (KJ) = 1 MegaJoule (MJ)

### Example 1

If a force of 20 N is used to pull a Wheelbarrow through a distance of 8 m. How much work is done in the process.

Solution

Work done = Force × Distance

Work done = $$\scriptsize 20 N \: \times \: 8 \\ \scriptsize = 160 J$$

### Example 2

A boy of mass 50kg runs up a staircase through a distance of 15m. Calculate the work done by the boy.

(Take g = 10m/s2)

Solution

mass of the boy = 50kg, Distance = 15m, g = 10 m/s2

Force = mass × gravity

Force = $$\scriptsize 50\:kg \: \times \: 10m/s^2 \\ \scriptsize = 500 \:N$$

Work done = $$\scriptsize Force \: \times \: Distance \\ \scriptsize = 500\:N \: \times \: 15\:m \\ \scriptsize = 7500\:J$$

1000 Joules (J) = 1 Kilojoules (KJ)

Therefore,

⇒ 7500 Joules (J) = 7.5 Kilojoules (KJ)

### Power:

Power is defined as the rate at which work is done. Power is the amount of work done divided by the time taken to do it.

Power is expressed as;

P =  $$\frac{W}{T}$$

Where W = Work done (J) and T = time taken (s).

Power = $$\frac{Work\: done}{Time} \\ = \frac{Force \: \times \: Distance}{Time}$$

The S.I unit of power is Joules per second (J/s) or Watt (W).

In the illustration above, we already know that the workdone in moving the box is 60Joules. It took 3 seconds to move the box with a force of 12N through a distance of 5m.

Therefore we can calculate the Power.

Power =  $$\frac{W}{T} \\ = \frac{60J}{3s} \\ \scriptsize = 20\:Watts$$

Watt Converter:

Larger units are Kilowatt (KW) and megawatt (MW)

1KW = 1000W

1MW = 1 million Watts (1,000,000) or 106 W

1MW = 1000 KW or 103

### Example 3

A gymnast lifts a mass of 85 kg vertically through a height of 5 m in 3 seconds. Calculate the power developed.

(Take g = 10m/s2)

Solution

mass = 85 kg, distance = 5m, time = 3 s

Power = $$\frac{Work\: done}{Time} \\ = \frac{Force \: \times \: Distance}{Time}$$

Force = $$\scriptsize mass \: \times \: gravity \\ \scriptsize = 85 \: \times 10 \\ \scriptsize = 850\: N$$

Work = $$\scriptsize Force \: \times \: Distance \\ \scriptsize = 850 \: \times \: 5 \\ \scriptsize = 4250\:J$$

⇒ Power = $$\frac{4250}{3} \\ \scriptsize = 1416.67 \: W$$

### Example 4

A motorcycle travelling at 30 m/s moves with a force of 650 N. What is the Power produced?

Solution

Power = $$\frac{Work\: done}{Time} \\ = \frac{Force \: \times \: Distance}{Time} \\ = \scriptsize Force \: \times \: \normalsize \frac{distance}{time}$$

But $$\frac{distance}{time} \\ \scriptsize = velocity$$

Therefore,

⇒ P = $$\scriptsize F \: \times \: V \\ \scriptsize = 650 \: \times \: 30 \\ \scriptsize = 19500 \: W \\ \scriptsize = \normalsize \frac{19500}{1000} \: \scriptsize KW \\ \scriptsize = 19.5 \: KW$$

### Energy:

Energy may be defined as the ability to do work. It can be transferred from one object to another by doing work. Anything that is capable of doing work has energy.

The formula that links energy and power is;

Energy = Power × Time.

The unit of energy is the joule, the unit of power is the watt, and the unit of time is the second.

Therefore,

Joule (J) = Watt (W) × Second (s)

Joule (J) = W*s

The main source of energy is the sun.

### Example 5

How much energy does a 40 Watt bulb use in 2 minutes?

Solution

Energy = Power × Time

Energy = ?

Power = 40 Watt

Time = 2 minutes

convert time to seconds

∴ Time = 2 × 60 seconds = 120 seconds

Energy = 40 × 120

⇒ Energy = 4800J

### Example 6

What is the power rating of an electric device that uses 5000 Joules in 50 seconds?

Solution

Energy = Power × Time

∴ Power = $$\frac{Energy}{Time}$$

Power = ?

Energy = 5000 Joules

Times = 50 seconds

Power = $$\frac{5000}{50}$$

⇒ Power = 100 Watts

The watt-second is a measure of electrical energy equal to one watt of power over a one second period.

Sometimes you will be asked to work with kW and hours not in Watts and seconds.

The equation will be as follows:

Energy = Power(Watt) × Time(Second) = Ws or J

Energy = Power(kW) × Time (hour) = kWh or KJ

### Example 7

How much energy does a 2kW heater use in 24 hours? Leave your answer in kWh.

Solution:

Energy = ? Power = 2 kW Time = 24 hours

Energy = Power(kW) × Time (hour)

Energy = 2 × 24 = 48 kW.h

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